What is $2\sum^2_{i=1}\sum^2_{j>i}a_{ij}x_ix_j$ is equal to?

Question

Intuitively I did: $$2\sum^2_{i=1}\sum^2_{j>i}a_{ij}x_ix_j=2(a_{12}x_1x_2)+2(a_{22}x_2x_2)$$

But I'm not sure, since I'm new to calculus.

Answer 1

There shouldn't be a second term, as the inner sum requires $j>i$ so $a_{22}x_2x_2$ is impossible. Unless, you meant $j\geq i$.